Black Bears, despite their size and strength, are typically very skittish and are not usually predatory, more being foragers and scavengers. In the majority of cases a black bear will choose to flee from an encounter with a human or even a dog immediately or can be easily convinced its not worth it, one notable exception usually being a mother with cubs which will fight to the death to protect them.
Grizzly Bears are more aggressive and are not likely to run from a threat, however they also don’t often prey on large animals unless they are rather hungry, so in the event that a violent encounter with a Grizzly is because you threatened it rather than its hungry, its most likely to leave you alone if it thinks you’re incapacitated. Its not very reliable though, especially with cubs around, but you’re unlikely to outrun or outmaneuver a grizzly in open terrain either. I’ve seen a lot of people suggest instead trying to slowly back away while seeming big but not provoking. The chances are about as good, but really you should always be armed in grizzly territory.
Polar Bears are very large, fully predatory, and not picky. They will almost always attack you on sight because food is scarce in the arctic, will pursue you, and where they live there almost never is cover of any sort so unless you are armed you are pretty much a goner.
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